how many grams of 206Hg will you have after 17.5 years?

Question

²¹⁰Pb has a half-life of 22.3 years and decays to produce ²⁰⁶Hg. If you start with 7.50 g of ²¹⁰Pb, how many grams of ²⁰⁶Hg will you have after 17.5 years?

The correct answer is 3.09

But I keep getting 4.35

Answer 1

Fraction remaining = 0.5ⁿ where n = number of half lives elapsed

number half lives = n = 17.5 yrs/22.3 yrs = 0.785

Fraction remaining = 0.5^0.785

Fraction remaining = 0.580

7.50 g x 0.580 = 4.35 g of ²¹⁰Pb left

7.50 g - 4.35 g = 3.1 g ²⁹⁶Hg